Attenuation of Shocks by Viscoelastic Support

The method of singular surfaces was used in a recent paper to develop a numerical procedure for calculating the growth and decay of the amplitude of shock waves propagating into a one‐dimensional nonlinearly elastic body. Here we extend this approach to estimate the influence of such external effects as elastic support and viscous friction on the propagation of shocks. We conclude that even in the case of a homogeneous linearly elastic material these external effects account for some attenuation of the amplitude of the shock and/or the secondary waves. Further analysis of a nonlinear elastic material readily shows that an increase in the viscosity produces, among other things, a slower growth of the shock amplitude and that for some critical value it will even start with a decay. Numerical examples illustrate the applicability of the technique in the case of a homogeneous nonlinear elastic body subjected to external viscous friction.